# History of Curves and Their Names

Here is some interesting history behind a few “good-looking” curves and how they got their names!

## Cissoid

Equation: $x^3 = y^2(a-x)$

The Cissoid is named so because of its resemblance to the shape of a Cissus plant. The Cissoid is a curve, defined as the set of points P that is the same distance from a fixed point F and a fixed line L. This curve is created by rolling a circle along a line, with the center of the circle always touching the line. The curve has a shape of a leaf of the cissus plant, and that’s why it got its name. It was first studied by the ancient Greek mathematician Diocles of Carystus in the 2nd century B.C. and later studied by the French mathematician Pierre de Fermat in the 17th century. It’s used in geometry and it’s also used in optics and engineering

It is important to note that the curve Cissoid was named by French mathematician Pierre de Fermat in the 17th century, and not by Diocles of Carystus as the curve was not known by him.

## Three-leaved Rose

Equation: $a\sin(3\theta)$.

The curve known as the three-leaved rose in mathematics is named so because of its shape. It has three symmetrical petals that resemble the shape of a rose. This curve is also known as the tricuspid curve and is a specific type of algebraic curve known as a cubic curve. It is studied in algebraic geometry and is used in various mathematical applications such as cryptography and computer graphics. The name three-leaved rose is given to this curve because of the three symmetrical petals that resemble the shape of a rose.

Interesting fact: Try plotting the same graph replacing 3 with 4,5,…!

## Astroid

Example: $x^{2/3}+y^{2/3}=a^{2/3}$

The Astroid curve is named so because of its resemblance to the shape of a star (aster in Greek). The curve is defined as the set of all points that are equidistant from a fixed point and the two foci of an ellipse. It is a specific type of algebraic curve known as a quartic curve. The curve has a shape of a four-pointed star, and that’s why it got its name. The astroid curve was first studied by the French mathematician Jean-Victor Poncelet in the early 19th century, and later by other mathematicians. It’s used in geometry, physics and engineering.

## Lemniscate of Bernoulli

Example: $r=a\sqrt{\cos{2\theta}}$

The Lemniscate of Bernoulli is named after Jacob Bernoulli, a Swiss mathematician, who studied it in the late 17th century. Lemniscate is a Latin word that means “ribbon” or “decorated ribbon” that describes the shape of the curve. It is a type of algebraic curve known as a quartic curve and is defined as the set of all points that are at a fixed distance from two fixed points. It looks like an infinity symbol and is symmetrical with two loops. The curve is used in mathematics and physics, particularly in the study of dynamic systems and potential fields.

## Cardioid

Equation: $a(1+\cos\theta)$

The Cardioid is named so because of its resemblance to the shape of a heart (cardio in Greek). The curve is defined as the set of all points that are equidistant from a fixed point and the focus of a given ellipse. It is a specific type of algebraic curve known as a quartic curve. The curve has a shape of a heart, and that’s why it got its name. The Cardioid curve was first studied by the French mathematician Jean-Victor Poncelet in the early 19th century, and later by other mathematicians. It’s used in geometry, physics, and engineering. It is also known as the Poncelet’s Cardioid.

## Strophoid $y^2=x^2\times{(a+x)\over(a-x)}$

The Strophoid is named so because of the Greek word “strophos” meaning “belt” or “girdle,” which refers to the shape of the curve. The curve is defined as the path of a point P on the circumference of a circle that rolls around the inside of a fixed circle, with P always touching the fixed circle. The curve resembles the shape of a belt or girdle and that’s why it got its name. It was first studied in 1831 by the French mathematician Michel Chasles and it’s used in geometry and mechanics.

P.S. The content was generated by ChatGPT – I just had the right questions! Mainly collected for the students with whom we discussed the same topic in class today/teachers who will be teaching the same topic in coming days! All the graphs were plotted with Python/Sympy/Matplotlib.

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